Suppose that a wideband pulse x(t) of finite duration and unknown shape is to be sampled at a plurality of J time instants t1, t2, . . . , tj, . . . tJ. It is assumed that the pulse duration is limited by some maximum value T, and that the pulse time-of-arrival is approximately known. The acquired samples of the pulse x(t) are then used to determine some pulse descriptors such as shape and its moments, including location and time spread. The pulse under examination may be regarded as being observed at the output of a suitable sensor that has captured a portion of electromagnetic radiation scattered by a remote object of interest.
A review of the development of sampling techniques is given in “50 Years of RF and Microwave Sampling” by Mark Kahrs, IEEE Trans. Microwave Theory Tech., vol. 51, no. 1, pp. 1787-1804, June 2003.
Conventional sampling techniques utilise ultra-fast sampling circuits to produce instantaneous signal samples. However, such ultra-fast sampling circuits are generally expensive.